Wavelet transforms found widespread application in signal denoising. Many adaptive algorithms were proposed to improve their performance, especially about edges in a signal. In this study, the authors propose a novel denoising method based on adaptive edge-preserving lifting scheme – intersection of confidence intervals-edge preserving lifting scheme (ICI-EPL). By incorporating the statistical method of intersection of confidence intervals rule into the lifting scheme, the authors are able to select the most appropriate wavelet on a point-by-point basis. The resulting transform adapts very well to local signal properties and significantly improves denoising performance. Simulations on various signal classes show that the ICI-EPL in most cases easily outperforms other considered transforms, with the greatest improvement being about edges in a signal. Achieved results bring confidence that the ICI-EPL can be used to improve performance in a variety of denoising applications.

In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising.

Blind source separation (BSS) problem is commonly solved by means of independent component analysis (ICA) assuming statistically independent and non-Gaussian sources. The strict independence assumption can be relaxed to existence of subbands where signals are less dependent. In this paper, we use dual tree complex wavelets for the subband decomposition of observed signals and small cummulant based approximation of mutual information for finding the most independent subband(s). We compare the proposed method to previously reported shift invariant and decimated wavelet packet based approach, as well as to innovations based approach. We found proposed dual tree wavelets scheme as an efficient and robust solution of the BSS problem of statistically dependent sources. One important application of the proposed method is related to unsupervised segmentation of medical and remotely sensed multispectral images.

In this paper, we explore the use of nonseparable and adaptive wavelet decompositions for the purpose of image denoising. We apply the classical wavelet shrinkage methods on the wavelet coefficients obtained by using the adaptive wavelet transform defined on the quincunx grid. The wavelet transform is pixel-wise adaptive in all decomposition levels. While providing more compact representation of the analyzed image, the adaptive transform retains some useful properties of fixed transforms, such as numbers of vanishing moments of primal and dual wavelets. The adaptive wavelet decomposition is realized using the lifting scheme. For comparison purposes, the image denoising results are presented for both fixed and adaptive wavelet transforms.

An efficient realization of a two-channel wavelet filter bank that maps integers to integers with an adaptive number of zero moments is presented. Filters with more zero moments result in a better representation of the smooth parts of the analyzed signal, while fewer zero moments are better for transients and singularities. The proposed realization is based on the lifting scheme that enables mapping integer signals to integer wavelet coefficients, preserving the perfect reconstruction property. The realization is derived from a method of fixed wavelet filter bank design, using Lagrange interpolation of samples in the time domain. The adaptation criterion is computed from integer wavelet coefficients, which is, under some restrictions, reproducible on the reconstruction side. Quantization introduces non-predictable components of the wavelet coefficients thus influencing the behavior of the adaptation algorithm. Adaptation on the interval is used to reduce the variance of the filter parameters.